* Horseshoes are attached, not worn: Unlike shoes we wear, horseshoes are nailed onto the hoof. They don't expand or contract with the hoof's growth.
* Hoofs grow continuously: A horse's hoof grows constantly, about a quarter of an inch per month. This means the hoof grows out from underneath the horseshoe, creating a gap.
* Farriers remove and re-shoe: A farrier (a professional who cares for horse hooves) will regularly remove the old shoes and re-shoe the horse, trimming the hoof and applying a new set of shoes to match the hoof's current size.
Therefore, horses need to be re-shod regularly, not because they grow out of them, but because the hoof grows underneath.